Get angle of point in circle with center $(0, 0)$.

Question

I have a circle with a centre at position $(0, 0)$ and I have a point in the circle at $(-5, 2)$. How can I get the angle of the point towards the centre?

I thought to use the theorem Al Kashi (law of cosines) but we need an another point to form a triangle but I don't have it.

Thanks, your help will be appreciated.

Answer 1

The angle, let's call it $\theta$, is in the second quadrant, so we have $\frac{\pi}{2}<\theta<\pi$, and from the given coordinates, we have $\tan\theta=-\frac25$. Is that enough information for you to determine the angle?

If you want to form a triangle for the law of cosines, you should choose your third point anywhere on the positive $x$-axis, because angles are measured from that reference direction.